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Moving window kriging with geographically weighted variograms

Abstract

This study adds to our ability to predict the unknown by empirically assessing the performance of a novel geostatistical-nonparametric hybrid technique to provide accurate predictions of the value of an attribute together with locally-relevant measures of prediction confidence, at point locations for a single realisation spatial process. The nonstationary variogram technique employed generalises a moving window kriging (MWK) model where classic variogram (CV) estimators are replaced with information-rich, geographically weighted variogram (GWV) estimators. The GWVs are constructed using kernel smoothing. The resultant and novel MWK–GWV model is compared with a standard MWK model (MWK–CV), a standard nonlinear model (Box–Cox kriging, BCK) and a standard linear model (simple kriging, SK), using four example datasets. Exploratory local analyses suggest that each dataset may benefit from a MWK application. This expectation was broadly confirmed once the models were applied. Model performance results indicate much promise in the MWK–GWV model. Situations where a MWK model is preferred to a BCK model and where a MWK–GWV model is preferred to a MWK–CV model are discussed with respect to model performance, parameterisation and complexity; and with respect to sample scale, information and heterogeneity.

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Acknowledgements

Research presented in this paper was funded by a Strategic Research Cluster grant (07/SRC/I1168) by the Science Foundation Ireland under the National Development Plan. The authors gratefully acknowledge this support. Thanks are also due to the first author’s PhD studentship at Newcastle University and to Professor Chris Brunsdon for kindly providing the R code for the comap. We also thank the anonymous referees whose comments and insights helped improve the paper.

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Correspondence to Paul Harris.

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Harris, P., Charlton, M. & Fotheringham, A.S. Moving window kriging with geographically weighted variograms. Stoch Environ Res Risk Assess 24, 1193–1209 (2010). https://doi.org/10.1007/s00477-010-0391-2

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  • DOI: https://doi.org/10.1007/s00477-010-0391-2

Keywords

  • Geostatistics
  • Kriging
  • Nonstationary
  • Nonparametric
  • Variogram